🤖 AI Summary
This work addresses the limited scalability of existing neural PDE solvers, which are hindered by high memory consumption and single-node bottlenecks that prevent application to meshes with tens of millions of nodes. The authors propose PGD-NO, the first neural operator architecture achieving linear memory scalability. By employing an iterative geometric decomposition algorithm to pre-extract geometric tokens, the method shifts geometric encoding to a deterministic preprocessing stage, thereby decoupling feature extraction from solution querying and circumventing single-GPU memory constraints. Integrated with an attention mechanism, PGD-NO enables efficient large-scale 3D physical field modeling while offering intrinsic interpretability. The approach attains state-of-the-art accuracy on multiple industrial benchmarks and successfully trains models exceeding ten million nodes, substantially surpassing the scale limits of current methods.
📝 Abstract
While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit. To address these challenges, we propose PGD-NO, a neural operator with Precomputed Geometry Decomposition, that relocates the computational overhead of geometric encoding to a deterministic pre-computation phase. By utilizing an iterative geometry decomposition algorithm to extract geometry tokens, our model decouples feature extraction from solution querying. This architecture enables linear memory scalability, allowing high fidelity learning on meshes exceeding 10 million nodes, a scale where existing architectures typically encounter memory exhaustion. PGD-NO demonstrates competitive predictive accuracy across diverse industrial benchmarks and provides intrinsic interpretability through attention mechanisms. By effectively overcoming traditional mesh-size constraints, PGD-NO offers a robust and efficient solution for the next generation of large-scale, high-fidelity industrial design applications.